In response to the criticism, Brewer has lashed out at President Obama who has called the new law "misguided" and ordered the Justice Department to see if it would violate civil rights.

Brewer said that five letters she's written to the federal government about her state's immigration issues have gone unreturned.

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Arizona Immigration Battle Heats Up

"I've spoke to the president personally in regard to [the letters], has been met with complete and total disrespect to the people of Arizona. I mean, we don't even get an answer back," Brewer said Monday.

Brewer said it was the state's way of working to solve a crisis that it did not create and which the federal government refused to fix.

"I firmly believe [the law] represents what's best for Arizona," Brewer said before signing the bill into law Friday. "Border-related violence and crime due to illegal immigration are critically important issues for the people of our state, to my administration, and to me as your governor and as a citizen."

Obama wasn't alone in criticizing Arizona's new law. Critics ranged from a former Arizona governor to the president of Mexico.

Mexico's foreign relations department issued an advisory today urging Mexicans in Arizona to "act with prudence and respect the framework of local laws."

"It should be assumed that any Mexican citizen could be bothered and questioned for no other reason at any moment," according to the travel alert.

"That one is a misguided law," Homeland Security Secretary Janet Napolitano told ABC News. Napolitano had vetoed the bill three times while she was governor of Arizona.

"It's not a good law enforcement law... But beyond that, what it illustrates is that other states now will feel compelled to do things, and you will have this patchwork of laws where we need a federal immigration system that meets our security needs, that recognizes where we need to go in this 21st century and gives us a better framework on which to stand," Napolitano said.

"The fact is that our borders are broken. They are not secure. It is a federal responsibility to secure our borders. It is not being done," McCain said on the Senate floor Monday.

The state capitol was vandalized when refried beans in the shape of a Nazi swastika was found smeared across it.

Democrat Chicago Alderman Daniel Solis had a similar message when he said "what has happened in Arizona is very similar to what happened in Nazi Germany."

President of Mexico Blasts Arizona Immigration Law

The president of Mexico expressed his anger with the legislation.

"My government cannot and will not remain indifferent when these kinds of policies go against human rights," President Felipe Calderon said.

Civil rights activist Rev. Al Sharpton promised even bigger protests if the lawsuit filed to block the law fails.

"We're going to bring people into the state of Arizona and refuse to show our IDs and openly walk the streets with people that appear Mexican," Sharpton said.

So far this year, Congress and the administration have made little progress in advancing immigration reform legislation, but Obama said Friday that if Congress failed to enact comprehensive reform, "We will continue to see misguided efforts opening up around the country."

The absence of a federal resolution of the controversial issue, he said, "opens the door to irresponsibility by others," and he cited "the recent efforts in Arizona, which threaten to undermine basic notions of fairness that we cherish as Americans."

Ariz. Immigration Bill Supporters Say They're Enforcing Law

The president has instructed the Justice Department to examine the Arizona law to see if it would violate civil rights. Other legal challenges are expected.

But even as the outcry continues, so does the applause from supporters of the law.

"Illegal is illegal," said Republican state Sen. Russell Pearce, who sponsored the bill. "We'll have less crime. We'll have lower taxes. We'll have safer neighborhoods. We'll have shorter lines in the emergency rooms. We'll have smaller classrooms."

Law Would Criminalize the Undocumented

Immigration reform has become a polarizing topic at all levels of government across the nation.

An estimated 12 million illegal immigrants live in the United States, and their presence is keenly felt in border states such as Arizona.

The Arizona law makes it a crime under state law to be in the U.S. illegally and allows police to arrest and question suspected undocumented persons about their status without a warrant. It also criminalizes the transporting of an illegal immigrant anywhere in the state, even if by a family member.

Brewer, who faces a tough Republican primary in August, signed the same bill that former Arizona Gov. Napolitano vetoed three times.

After the signing, crowds outside of the state capitol building erupted in anger. Carrying signs and American flags, they marched nearby, protesting the governor's decision.

Thousands of people wrote or called the governor's office, with a 10-to-one majority opposing the bill, a spokeswoman said.

"I don't think anything has been this extreme until this point," said Bridgette Gomez, a 24-year-old math tutor. "The evil is racial profiling, to think that you're going to always have to show identification. Because I'm tan, I must be illegal."

The Arizona bill takes effect in 90 days after the current legislative sessions over the next several weeks.